wind tunnel calibration

7/28/2019 Wind Tunnel Calibration

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FILECOPYNO. I-Wn

NATIONALDVISORyOMMITTEEORERONAUTICS

WARTIMEREPORT ORIGINALLY I S S U E D October$kksAdvanceRestrictedReportAE31

WIND-TUNNELALIBRATIONN DORRECTIONROCEDURES FORHREE-D IMENSIONALMODELS

ByRobert.wansonandClarenceL.Jillis


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NACAARRNo .L4E31 RESTRICTEDNATIONALADVISORYCOMMITTEEFORAERONAUTICS

ADVANCE.RESTRICTEDREPORTWIND-TUNNEL CALIBRATIONANDCORRECTIONPROCEDURES

FORTHREE-DIMENSIONALMODELSByRobertS .SwansonandClarenceL .GIllIs

SUMMARYDetailedmethodsarepresentedfordeterminingthecorrectionst oresult?fromwind-tunneltestsofthree-dimensionalmodelsfortheeffectso fthemodel-supportsystem,thenonuniformairflowinthetunnel,andthetunnelwallsorjetboundaries. Theproceduresfo rdeterminingthecorrectionsareillustratedbyequationsandtherequiredtestsarediscussed. Particularatten-tion" I sgivent othepartsoftheproceduresdealing withdragmeasurements. Twogeneralmethodsthatareusedfordeterminingandapplyingthecorrectionst oforce


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^ ACAARRNo .L4E31Theusualpracticeo fpredictingtheflyingqualitiesofairplanesfromwind-tunneltestso frelativelysmall-scalemodelsmakesi timperativethatthemodeltestresultshecorrectedt ofree-airconditions. Inaddition,thelargenumbero fwindtunnelsinusemakesi tdesirablethata moreo rlessstandardcalibrationandcorrectionprocedurebeadoptedinordertomakedatafromdifferenttunnelsasnearlycomparableaspossible. Notmuchcom-prehensiveinformationhasbeenpublishedpreviouslyonthesubjectofwind-tunnelcalibrationandcorrectionmethods. Thediscussioncontainedinreference1i sprobablytheb e . " tinformationt odate. Adiscussioni sgiveninthepresentreportofthemethodsinuseatthepresenttimeforcalibratinga windtunnelanddeterminingthecorrectionst obeappliedt othemeasuredmodeldata.Somerefinementst otheusualproceduresaresuggestedwithspecialattentiontothosepartsoftheprocedurethataffectt h edragmeasurements. Theuseo flargemodelsinordert omorenearlyapproachtheReynoldsnumbersobtainedinflighthasincreasedthemagnitudeandthustheimportanceo fthejet-boundarycorrections.Adetaileddiscussiono fjet-boundarycorrectionsisnotgivenherein,however,becausethi* 1subject,exceptfo rtheeffectsofcompressibility,hasbeentreated


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NACARRNo .L4E21 :

SYMBOLSCLiftcoefficientC jectionliftcoefficientLiftIectionliftCDragcoefficientC - nrofile-dragcoefficientc^ectionprofile-dragcoefficientDragd ectiondragC^ esultant-forcecoefficient


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4 ACAARRNo .L4S31

v ' effectivevolumeofbodyforstatic-pressure-gradientcorrections(denotedby' inreferences2and3 )5ingareabingspanc wingchordy spanwisedistancefromcentero ftunneli ^ . angleo fincidenceofhorizontaltailsurfaceTbsolutestagnationtemperatureatlow-speedsectiono ftunnelTabsolutetemperatureattestsectionoftunnelh tatic-orificepressuredifferencep taticpressure


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NACAARRNo .L4L31SubscriptsInlinement-angleequations;S scalereadingE erect-modeltestI Inverted-modeltestav averageweighted according to span-loaddistributionInareequations:1estofmodelontaresupport2esto fmodelo ntaresupportwithdummysupportInplace3estofmodelonnormalsupport


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I I AC AARRNo.L4E31them od el-s upp ortsystem,then on un if ormair-flowcondi-tionsinthetunnel,andthetunnelwallso rjetbounda-ries.

Tares. -Thecorrectionsf o rtheeffectso fthemodel-supportsystemareusuallydeterminedInthef o r mo fincrementso fforcesandmomentso rthecorresponding coefficientsandarecalledtares. Thetaresarecom-p os edo fthedirectairforceso nthesupportsystemplusthemutualinterferencebetweenthesupportsystemandthemodel. Itcouldbeexpected,therefore,thatthetareswould begreatlydependento nthesizeandshapeo fsupports,thec on figurati ono fthemodel,andthepointo fattachmento fthesupportstothemodel.Therelativelygreateffecto fthemo de lc on figurati ono nthetaresisillustratedinfigure1 ,whichpresentssometarevaluesmeasuredIntheLangley7-by10- f o ottunnelf o rtwodifferentmodelsunderseveraltestcon-ditions.

Becauseo ftheirdependenceup onthesupportandmodelconfiguration,thetaressho uldbedetermined


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MACAARRNo .L4531( 3 )AvariationIntheair-flowangleInthe

regionoccupiedbythemodel. Thechangeintheaverageairspeedalongtheaxisofthetunneliscaused byanyactualoreffec-tiveconvergenceordivergenceoftheairstream.Thischangeinvelocityalongtheaxiso fthetunnelcausesavariationinthestaticpressureandacorrec-tionmustbeappliedt othedragtoaccountforthebuoyancyeffectofanysuchstatic-pressuregradient.

Fo ranopen-throattunnelthepossibilityofhavingadivergingorconvergingairstreami sobvious. Fo raclosed-throattunneltheformationo fa boundarylayeralongthewallsofthetestsectionchangestheeffec-tiveshapeofthetunnel. Closed-throattunnelsareusuallydesigned withaslightlydivergenttestsectiontocounteractthiseffectbutinanycasethestatic-pressuregradientmustbemeasured. Thetunnelleakageconditionscanhaveaverymarkedeffecto nthestatic-pressuregradient(references2andZ) becausealeakinthetunnelchangesitseffectiveshape. Allholesinthetunnelwallsofthetestsectionshouldthereforebesealed. Ifsealingi snotpossible,theamountofleakageshouldbemaintainedasnearlyconstantaspos-


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8 ACAARRNo .L4E31Inasmuchas e Isasmallangle, cos 1.0nd

Therefore,Cr=Ros p - 5775R sin

sin -Tr-^' Therefore,

(1)Similarly,

GD R sin ( + e) = CR (sin cos e + cos 8 pin e)=R sin 3 + gTjr-jRos ~ CDS + 5773 GLS 2

Thisderivationmay beappliedt oeithertheerect-modelo rinverted-modelconditionasindicatedinfigure2 .


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NACAARRNo .aclo^et^-throatt u n r . e ltheoffectofthetunnelwallsisgenerallyt olimitthedownwasharoundthemodelandthustocauseaneffectiveupwarddeflectionandanupwardcurvatrreoftheairstream. Adisplacementclockingoccursbecausetherigidwallsalsoprohibittheexpansionoftheairstreamasitpassesaroundthemodeland,astheairisconstrainedt oasmallercross-sectionalarea,thevelocitycorrespondinglyincreases.Thisincreaseinthevelocityi sgenerallyconsideredseparately. Fo raropen-throattunnelaphysicalinterpretationo fthejet-boundaryeffectsmaybeobtainedbyconsideringthatthemassofmovingairwhichi saffectedbythemodelisno ts olargeasthemasswhichwouldbeaffectedifthemodelwereinanunlimitedairsbream. Theairstreamthusundergoesagreaterdeflectionandcurvatureandagreaterexpansioninpassingoverthemodelthanitwouldexperienceifitwereo finfiniteextent. Theeffecto fthejetbounda-riesfo ranopen-throattunnelisthereforegenerallyofoppositesignfromtheeffecto fthetunnelwallsfo raclosed-throattunnel.

Thesubjectofjet-boundaryinterferencehasbeen


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10 ACAARRNo .I4S31blockedo ffbythemodel. Thissimpleempiricalfactorwasderivedfromtheresultso funpublishedtests-todeterminetheblockingcorrectionfo rthelifto ftwo-dimensional-flowmodelsa swellasfromresultsofafewtestst odeterminethecorrectionsfo rthree-dimensionalwings. Itshouldbenotedthatthedataonblockingcorrectionsforsymmetricalbodiesgiveninreference2indicatethatthecorrectionvariesasthesquareo ftheareablockedo f f , whereastheexperimentaldataonliftingwingsindicatethatthecorrectionvarieslinearlya sthearea blockedoff. Thenumericalvaluesareroughlythesane,however,fortheusualmoderate-sizemodels. ThesimpleruleforestimatingthecorrectionI sfairlyaccurateforaerodynamlcallycleanbodiessuchasplainwings. Fo rbluffbodieso rbodieso fanyotherformthatcreatesalargewake,suchasa wingwithasplitflap,anadditionalcorrec-tionduet othestatic-pressuregradientgenerated bythewakeshouldbemadea soutlinedinreference2 .ThisadditionalcorrectionisIngoodagreementv / i t htheexperimentallydeterminedadditionalcorrectionobtainedfromthetestswithsplitflapsdeflected.

The of for


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MCAARRNo .L4E31determinationo fsatisfactorycorrections. Foranyt u n n e l ,however,thenumericalvalueo ftheturbulenceshould beknowninordertofacilitateacomparisono fthedata withdatafromotherwindtunnelsorfromflighttestsort ostudyfurthertheturbulenceeffects. TheReynoldsnumberandMachnumberarealsoquantitiesforwhichnocompletelysatisfactorymethodsofcorrectionhavebeendevised.Fo rpurposesofcomparisonwithotherdata,theirvaluesshouldbeknown,however,andspecifiedforallmodeltestsforwhichtheyarelikelyt ohaveaneffect.B e c a u s ethesupportsystemcauseslocalchangesintheairflow,itmaybedesirableforsometests,inwhichMachnumbereffectsareespeciallycritical,tospecifynotonlytheaverageMachnumbero ftheairflowbutalsothelocalMachnumbersnearthesupports.

CorrectionMethodsThesuccessfulapplicationofcorrectionst owind-tunneldataisdependento nthetypeoftunnelusedfortesting. Twomethodsareavailableforgeneraluseandforconveniencearedesignatedherein method A and method B .MethodA ,whichisbasedonaclear-tunnela i r - f l o w survey,


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12 AG AARRNo.L4E31effectsofthesupportsystemandthenonuniform!tiesIntheairstream. Ifthelet-boundarycorrectionsareappliedalongwiththeblockingcorrections,thedatathenrepresentthemodelinanunlimiteduniformairstream. Although,properlyspeaking,theblockingcor-rectionI saneffectcausedbythepresenceofthetunnelwallsorjetboundaries,itIsmosteasilyappliedinthesecondstepsimplyasacorrectiont othevalueof qsedIncomputingthecoefficients. Onevariationfromthisprocedure,whichi ssometimesused,istoapplythelet-boundarycorrectionsbeforethetarecorrections. Thetaresmustthenbecorrectedfo rjet-boundaryInterference. Thedifferenceintheresultsfromthetwomethodswillgenerally benegligible.Inthisreportthetareswillbedetermineds othattheymay beappliedfirst.

MethodE. -Ashasbeenpreviouslynoted,method Bisbasedonanair-flowsurveywiththesupport strutsinplace. Thetaresdeterminedbyuseo fthismethodIncludeanyeffectso fthesupportsystemthathaveno tbeenaccountedfo rintheair-flowsurvey. Ifthebasic .


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NACRRNo .L4E31 3correctiontothevalueof sedfo rcomputingthecoefficients.

Atpresentnosatisfactorymethodo f measuringthechangeso nair-flowangleandstatic-pressuregradientcaused bywakeshadowha?beendevelopedandtriedexperimentally. I f ,therefore,anydifficultiesresultingfromwakeshadowarefoundtoexistina windtunnel,thebestprocedureprobablywouldbet omodifythetunnelbyaddingscreensordiffuservanesinsuchawaythatthewakeshadowwouldbeeliminated.

Thewakeshadowneedno tnecessarilypassdirectlyoverthemodeltocauselargeerrors. Forexample,ifthewakeintravelingaroundthereturnpassagesi sdeflectedwellbelowthemodel,i twillpassnearthestaticorifices(usedt oindicatethedynamicpressure)onthefloorofthetunnel. Ifthestaticorificesont hwillthengiveerroneousindicationsofthedynamicpressure. Itmightbenotedthatifthedifferenceinairpressurebetweentheorificesi slarge,theairflow

nthefloorofthetunnel. Ifthestaticorificesntheroofandfloorareno tconnectedsymmetrically,heresultingairflowthroughtheconnectingtubes


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14 ACAARRNo .L4E31

strutsmustalsoberemovedfromthetunnel. Fo rcorrec-tion method E ,thesupportstrutsmustremaininthetunnel. Thefirstsourceo finaccuracyo fthesecondsystem mayhementioned here. I tisdifficultt omeasurethedynamicpressurenearandatthesupportsystembecause,inpractice,parto fthesupportsystemisenclosedinthemodelandanychangesinvelocitycausedbytheseotherwiseenclosedpartsarethuserrors.Theair-flowsurveysshouldbemadeoveraplaneperpendiculart otheairstreamatthepositiont obeoccupiedbythewingo fa modelt obetested. Usuallythispositioni sat,orverynear,thesupport-strutlocation. Thesurveyshould bemadeatvariouspointsonalineacrossthetunnelatseveralheightstocoverallpossiblemodelvariations. Thisoriginaltunnelsurveyshouldbemaderatheraccuratelyandcompletely.Unlesssomealterationsaremadetothetunnelo runless

s o m e ,changeintheair-flowconditionshasbeenindi-cated,onlyoccasionalchecksurveyswillbenecessary.Themeasurementsoverthissurveyplanemaybemadewithacombinedpitch,yaw,andpitot-statictubeand


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MACAARRNo .L4E31 5

inthealinementangleof0.25willcauseanerrorinthedragresults,of. 0 O 4 4 C J ; , , whichi sexcessive.Thealinementangleateachsection may hedeterminedsome-whatmoreaccuratelyhyuseo fafairedcurvethroughagreatmanypointsobtainedby repeatingthetests. Thedifficultyinobtainingmoreaccuratereadingsi sprobablycausedmainlybythelackofsufficientrigidityinthemountingsupportfo rtheyawheadandbytheerrorsmadeinmeasuringtheinitialsetting. Thesupportshouldthereforebedesigned withthegreatestcare;asupportspanningthetunnelratherthanacantileversupports h o u l dbeused. Erectandinvertedyaw-headtestswiththesamemountingsystemaredesirable. Becauseoftherelativelylargeinaccuracyoftheyaw-head measurements,thealine-mentanglesare'generallydeterminedfromactualmodeltests,asi sshownlaterinthesection"Alinement-AngleCorrections." Thealinementanglermeasuredbytheyawheadmaystillbeofvalue,however,ifthevariationinangularityacrossthetunnelisgreaterthantheaccuracyo fmeasurement. Theyaw-headmeasurementsmay beadjustedtoagreewiththeaveragealinementangleasdeterminedfromthemodeltestsandtheresultingvariationmaybeusedt ocomputethealinementangleforeachmodel,aswillbeshownindetail.


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16 ACAARRNo .L4E31

severaltunnelairspeedsbecausetheIncreasedtunnelandmot orvibrationsthataccompanyariseintunnelspeedoftenappreciablyincreasetheturbulence.Foranextremelylow-turbulencetunnelwithcon-ditionsapproachingfree-aircondition.?,thehot-wiremethod becomesInadequate"becausevariousdisturbingInfluences,suchasthevibrationo fthewire,causereadingst obehigherthanthosecaused byturbulence.ComparativeturbulencemeasurementsInsuchcasesmaybeestimatedfromtestsoflow-dragairfoilsthatereverysensitivetochangesinturbulence.

CorrectionsOncethetunnelcalibrationsarecompleted,thespecificcorrectionsaffectingtheaerodynamiccoeffi-cientsmayhecomputed.Dynamic-pressurefactor.-Inordert odetermine

thedynamic-pressurefactor,thevalueo f easuredateachpointo nthesurveyplanei sdividedbythestatic-orificepressuredifference ndthevaluesof/ hreplottedagainst. thedistanceacrossthetunnelinaspanwisedirection. Acurvedrawnthroughthepointsgivesthedynamic-pressurevariation


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NACAARRNo .L4E31 17Ifthemethodo ftunneloperationissuchthati tispossiblet omaintainagiven uringatestrun,thisproceduremaybereversedandthevalueof obeusedcanbecalculatedforanydesired. Curvesmaybeplottedof gainst sfoundfromequa-tion( 4 )forawiderangeofmodelspansandplanformsandthedensityofthemanometerliquidshouldbetakenintoaccount. Useo fthesecurveswillsavetime,astheymakeitunnecessaryt ocompute r oreachtestoreachtestpoint.

Correctionstothevalueo f fortheeffectsofwakeblockinganddisplacementblockingmustbemadeiftheseeffectsarefoundtobeappreciable. Thesecor-rectionsdependuponthemodelconfiguration,however,andarethusno tconcerned v / i t htheclear-tunnelcali-bration.Atspeedsinthecompressiblerange,theimpact

pressure -p , determinedfromtheair-flowsurveys,i slargerthanthetruevalueof. Thecorrectedqaybefoundfromtherelation


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1 8 KACAARRNo .L4E31testsection. Theu^uelmethodist omeasurethetem-peratureatthelow-speedsectionaheadoftheentranceconeandtocalculatethetest-sectiontemperaturefromtheequation

V-lTa ~h- p \ r ( 8 )Thecorrectdensityisthen

_1HA IP_RT ' s*) A ( 9 )Asthecorrectvalueofboth and areno wknown,thevelocitycanbecalculated."Thevelocitymayalsohecommutedfromtheformula


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NACAARRHo .L4E31 9u s e d ,onlywithcorrectionmethod A ,however,isusuallydeterminedfromtwotestso na modelwing. Onetestismadewiththemodelmountederectandtheothertestwiththemodelinverted. Fromfigure2(a)andthederi-vationo fequation( 2 ) ,thecorrectdragcoefficientfo rtheerectmodeli s

CD=CDg +CL 5773 ( 1 1 )

Thesignsofallcoefficientsandanglesaretakenwithrespecttothetunnel.o rtheinvertedmodel( f i g . 2 ( b ) ) ,thecorrectdragcoefficientisCD=CD CL1 2 ) ^> T157.3

Ifallothereffectshavebeenaccountedforexceptthealinementangle,thetwodragcoefficientsmustbeequalatagivenliftcoefficient


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20 ACAARRNo .L4E31linefairedthroughthepointsismultipliedby57.3/2toobtaintheaveragealinementangleIndegrees. Theaccuracyofthisproceduredependsuponthefactthatallothereffectshavebeencorrectlyaccountedfor. Iti snecessarythereforet oaccountforthetareswiththeu t r r o s tprecision. Inordertoavoidactuallydeterminingandapplyingthetarecorrections,however,thetestsforbotht h eerectandinvertedmodelsaremadewithanexactseto fimagesupports(fig.3 )mountedontheoppositesideo fthewingfromthenormalsupports. Thetaresarethusautomaticallyaccountedforbythistestprocedure.ItisalsoveryimportantthattheleakageeffectsaroundthesupportstrutorfairingbeexactlyreproducedInthedummies. Testsintwodifferentwindtunnelshaveshownerrorsofa smuchas0.25 Inthealinementangleduetoincorrectleakagereproduction. Theaverageallne-mentangledeterminedInthiswaywillbeweightedaccordingtothespanwiseloaddistributionascanbeseenfromthefollowingderivation:

AtanysectionAd=l e


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NACAARRNo.L4E31 1where sthedragcorrectionatzeroliftandwill" b e zeroifthewinghasnoaerodynamictwistandthevariationof e acrossthespanisnotgreatenoughtoresultinaneffectiveaerodynamictwist. I fthealinemcntanglevariesappreciablyacrossthemodelspan,theaveragevaluewillthusbedifferentfordif-ferentwingconfigurations. Fo rthisreason,alinement-angletestsarefrequentlymadeindividuallyfo reachmodeltested. Itisbelievedthattheextratimerequiredwiththisprocedurei sunnecessaryandthattheaccuracy may beincreasedifalittlemoretimeandcarearetakenintheoriginaltunnelcalibrationt odeterminethealinementanglefordifferentwingconfigurations.Severalwings,ofdifferentspansandplanformsandpreferably withtransitionfixed by meanso ftransitionstrips,shouldbetestedwithandwithoutpartial-spanflapsinordert odeterminethealinement-anglevaria-tionwithwingconfiguration. Becausethedragcoeffi-cientsarecomparedataconstantliftfo rtheerectandinvertedmodel,theairfoilsectionused willhavenoeffectontheresults,unlesstheairfoildragisunusuallysensitivet otransition,surfaceroughness,andsoforth. Inthiscase,much morecarei srequired


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I : AC AARRNo .L4E31

Thealinernentanglet o beusedforcorrectingtheangleo fattackI sno tquitethesameasthatto heusedt ocorrectthedragbecausedifferentmethodsofaveragingthealinernentanglesshould beusedfo rtheliftandforthedrag. TheerrorInusing eav astheangle-of-attackcorrectionI susuallysmall,however,s othatthes a m e -anglemaygenerallybeusedfo rcorrectingtheangleo fattackasi susedf o rthedrag.

Po rthecorrectionmethodB ,thealinernentanglet obeusedshouldbethatwiththesupportsInthetunnel. I ti scustomaryt ousethealinernentanglesmeasuredbytheyawhead. Incaseaccuratedragmeas-urementsaredesiredatmoderateorhighliftcoeffi-cients,thisprocedurewillprobablynotbesufficientlyaccurate. Apartialover-allcheckonthefinalaccuracyofthissecondproceduremaybeobtainedbycomparingthefinalfullycorrecteddataobtainedfromerect-andInverted-modeltestso fsymmetricalwingmodels.IfanydifferenceexistsInthemeasuredalinernentanglesatthepositiono fthewingandthetail,acor-


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NACAARRNo .L4E31 3

requiredt ominimizeinterferenceeffects. AtMachnumbersatwhichthesupportsorpartso fthemodelnearthesupportshavereachedacriticalspeed,thedifficultiesa j ^ - uncertaintiesinobtainingtaresbecomeexcessive. Nosatisfactorytechniqueforobtainingsupporttaresatsupercriticalspeedshasyetbeendeveloped.Buoyancyc orrectio n. -Arextensivetheoretical

investigationoftheeffectso fastatic-pressuregradientwillbefoundinreferences2and3 . Mostclosed-throatwindtunnelsaresodesignedthatthestaticpressureintheregiont o beoccupiedby amodelisconstantand nocorrectioni srequired. Ifagradientdoesexist,thedragcorrectionIsproportionaltotheproducto fthegradientandtheeffectivevolumeofthebody,andtheproportionalityfactordependsontheshapeo ftheb o d ; / . Agoodapproximationtothecor-rectionfo rathree-dimensionalbody maybefoundfromtheequation


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24 ACAARRNo .L4E31Twopossiblewaysareavailableforrunningthetests. Themodelmay bemountedinthenormalpositiononanauxiliarytare-supportsystemconstructedtomeasureallforcesandmoments;oretestm>f berunwiththenormalsupportso rdummysupports[exactimagesofthenormalsupports)I nplaceandanother withthenormalsupportsordummiesremoved. Anothermethodi sto mountthemodelinverted o nanauxiliarytaresupportoro nthenormalsupports,whichthenbecomethetaresupportsforthetaretests,withdummysupportsconnectedt othemodelfo ro netestandremovedfo rthesecondtest.Abasisfo rthediscussionoftare-testprocedurewill beprovided bysomegeneraltareequationsrepre-sentingcorrection methodAwithalltestsrunwiththemodelinthenormalposition. ThederivationIssome-whatarbitrary,especiallywithresnecttotheinter-ferenceterms. Themainpurposeo ftheequations,however,i stoshowtheinaccuraciesandapproximationsinvolvedintheusualtaredeterminationsandtoindi-catemethod?ofImprovingtheaccuracy. Fo rthispurposeanyo fseveralwayso fwritingtheequationswillgive


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NACAARRNo .14331 5

Fo rthederivation,themodeli sassumedtobemountedinthenormalerectposition withthetareanddummysupportslocatedo nthesamesurfaceofthemodel(fig.4). Foractualtestworkthetare-supportsystemshowninfigure4(b)maynotbesatisfactorybecausetheinterferenceeffectsbetweenthetareanddummysupportsma3 rbeexcessive. Theeffecto ftheinterferencewillbeshownbytheequations. Thetare-supportsystemshownIsusedforIllustration,however,becausei tgivessimplerequationsthanforthecaseoftheinverted model.Thechangesintheequationsrequiredfo rthecaseoftheinvertedmodel(fig.5 )willbeIndicatedlater. Thesignso fallforcesandanglesaretakenwithrespectt othetunnelratherthanthemodelaxes. Fromtestsofthemodelaloneontaresupport(fig.4(a)),C D]Sq=DM(l+5 T)+DT( 1+6M) +Djm- (e+A eT)cLlSqwhereC j ) , Sq dragscalereading,poundsC^Sq liftscalereading,pounds


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26 ACARRNo. L4E31

_%(l + 6T)(lj-5 DT(l + 5M)(l + D)DD(l + 5F)(l+ T) Dl C1 + 5T )

Sq i^_ +

PTMT(I 5P) DlTD(l + 5M)S qq- CLo(e + AeT + Acr 19)

The tare is takens A C D ~CD -D&CDD=CDM[(1 T)(l 4 - 6D - (l - 6T)]


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NACAARRN o .L 4 E - 3 1 7Ifthedummysupportsareexactimagesofthe

normalsupport( a stheyshouldbe)or,betteryet,ifthenormalsupport"Insteadof dummieshavebeenused,alltermswithsubscript illbeequalt othecorrespondingtermswithsubscript. Themodelcoef-ficientcorrectedfo rthetaredragispACD then

D =% I

1 + 5 D ) " C1

+ MC

1

+

5D )

+ ( 1

+ 5 T ) ]+ ^1 + 6 M ) - C 1 + 5 D ) ( ] + 8 M ) ]

- % * D " J +5M) " < L 3 " C L 2 + C Ll )T - LTD


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2 8 ACARRNo .L4E31Ifthetaredeterminationsaremadewiththemodel

mountedinverted,itisassumedthatthetaresupportsareinthesanepositioninthetunnelf o rthesetestsasfo rtheerect-modeltestswiththedummysupportso ntheoppositesurfaceofthemodel. (Seefig.5 . ) Thesignsofsomeofthetermsarereversedfo rthetaretestswiththemodelinverted. Inthiscasealso,thelifttareis ACT =C T -C T InsteadofT -C Thil L22lasfo rthetaretestswiththemodelerect. Inthefinalliftequationalltermsthatarisebecauseofthepresenceofthetaresupporthavetheoppositesignfromthatindicatedinequation( 2 2 ) . Fo rthedragequation,thesignsofsomeofthealinement-angletermsaresoreversedinthederivationthattheequationwillhe

CD-

CDS"

ACDD

= CDM0- - 5T5D) ~ CD T C1 + M)D " ^nC1 + 6M )5T


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NACAARRNo .L4E31 9fromanair-flowsurveywiththetaresupportsinplace,alltermsmultipliedby. p inthefinalequationwillbeeliminated. Thefactor 1+5 < pillaffectsomeo ftheothertermsIntheequationandtheequationbecomes

C 1+p)CI > n CDT-M T n+6i v i \cvi+TyTD-e CL +ATACID+ACDACLT 2 4 )

withthesamechangesaspreviouslynotedfo rthetaretestso ftheInvertedmodel. Thefactors r p and 6 ^willbeo ftheorderof0.03t o0.05andallundesirabletermsno wremainingintheequationaresecond-ordereffectsexceptthe C - n T term,whichi ssmalliftheJ- T D


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30 CAARRNo .L4E31support?areattachedtothemodel. ThequantityT} _ismoredifficulttoestimate.

Thefactornaybefoundquiteeasily by acom-parisono fthedynamic-pressuresurveysmadeforthecleartunnelandthesupports-in-placecondition. ThequantitiesCpAC-^ andeDACT alongwiththeinter-ferencefactorr,~remutualinterferenceeffectsTTDbetweenthetwosetso fsupportsthatmustbedeterminedo reliminated. Inmostcases,theerrorscausedbyneglectingtheinterferenceeffectswillbewithintheaccuracyo fmeasurement. Fo rexample,whenavalueo ftareliftequalt o0.02(fig.1 )isused,achangeo falinementangleof0.3atthewingliftinglinewouldcausetheIncremento fdragcoefficientfromtheA c r p A O j termintheprecedingequationst obeapproxi-mately 0.00C1. The AeDCj termshouldbeofthesameorderofmagnitude. Anexaminationo ftheavailable


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NACAA R E 'No .L4E31 1supportst oreducethemutualinterferenceeffectsareshownInfigure6 .

Fromaerodynamicconsiderations,awiresupportsystem(fig.6 )satisfiesratherwellmosto ftherequirementsforagoodtare-supportsystem. Wire'supportscauselittlechangeinair-flowangularityandlittlechangeindynamicpressure. Severalobjectionst oa wiresupportsystemareevident: Notalltunnel-balanceframeaares oconstructedthatthewiresystemmaybeused;thewiresmustbepreloadedthesamefo rbothtaretestsinordert oeliminatechangesinwiredragduet uchangesinwiretension;thelargedragofthewiresdecreasestheaccuracyofdeterminingthetaredrag;andtheinstallationo fa modelwithawire balancei sdifficult. T naddition,thewiresupportsystem willprobablyhavealo wcriticalspeedandcannotbeusedwhenhighT I a o hnumbersarerequired. Thesupportsystemshowninthecenteroffigure6willprobablyalsobe'unsatisfactoryfromacompressibility*standpoint. Ithasbeenfoundthatthewiug~tipsupportsmustbedesignedtoavoidappreciablelifttaresjthati s ,thecrosssectionmustbecircularorsomesimilarshape. Thecriticalspeedofsuchastrutwouldthen below. Ifthetwosetsofsupportsareplacedatadistancefromeachother,it


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32 ACAARRNO.L4E31

normalsupportInplaceandIncludestheeffectofthesupportson and e . ThetaresshouldthereforenotIncludeanychangesin and e causedbythesupports. Thetares" inthiscasearethendefineda sthedirectairforceso nt h e *supportsplustheinter-ferenceofthemodelonthesupportsplusanylocaleffectso fthesupportso nthemodelnotincludedIntheair-flowsurvey,suchastransitionchangesorseparationeffectso nairfoilsatthepointo fattach-mento fthesupporttothemodel.Thedirectairforceso nthesupportsandtheinter-ferenceo fthemodelonthesupportscanbemeasuredbymountingthemodelindependentlyofthebalanceby meansofcablesandmeasuringtheforcesonthebalance. Inordert omeasuretheeffectso fthesupportsontransi-tionandseparationchangesontheairfoil,iti sneces-saryt ohaveaseto fdummysupports. ThemodelIsplacedo nthetaresupportsornormalsupportsandthe

dummiesareplacedcloset o ,butnotincontactwith,themodel. Thedifferencebetweenthistestando newithoutthedummiesgivestheinterferenceeffectofthedummies. AnexampleofthisprocedureinuseintheLangleyfull-scalptunnelI sshowninreference1 9 .


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NACAARRNo .L4E31 3

Wakehadow .-A3statedpreviously,thewakeshadowmaycausechangesIntotalhead,static-pressuregradient,dynamicpressure,alinementangle,andturbu-lence. Theexistenceofa wakeshadowmay hedeterminedquiteeasilyfromtotal-pressuresurveysmadeatsomesectiono fthetunnelaheadofthemodelandcomparedwithtotal-pressuresurveysatthesamesectionwithnomodelInthetunnel. Thesurveyshouldhemadeovertheentiretunnelsectionatthesurveyplane,especiallynearthestaticorificesincasethewakei sdeflectedfromthecenterofthetunnel.Ttwouldseemthatnoexactsolutionoftheprob-lemsofwakeshadowi spossible. Onemethodofesti-matingthevalueof qhenwake-shadowblockingI spresenti sthatusedattheLngleyfull-scaletunnel.Thistunneliso ftheopen-throattypeandithas beenfoundthatthestaticpressureatthemodelpositionwithonlythesupportstrutsInthet i i n r e li sequaltothepressureInthetestchamber. Fo ranyparticularmodelthetotalpressureoveraplanesomewhataheadofthemodelandthestaticpressureinthetest


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34 ACAAHRNo .L4E31

thebalancesystemonwhichthemodelifmounted. Inordertodeterminethevariationoftheprofiledragalongthewingspan,wakesurveyt e s t , "areoftenmade.Thesesurveyshavealsobeenusedt odeterminethecom-bineddragtaresandbuoyancycorrectionsfo rsomemodels(reference20). Thismethodoftestingrequiresconsiderablymoretimethanforc^testsbuti stheonlywayo fdeterminingthevariationofprofiledragacrossthewingspan.Fo rthewakesurveys,theeffecto fthesupportsisaccountedforbycomputingcoefficientsbyuseo fadynamicpressuredeterminedfo rtheair-flowsurveysmadewiththesupportsinthetunnel. Theactual teachpointalongthespanratherthantheaveragevalueo fmustbeusedfo rdeterminingthelocalprofile-dragcoef-ficients. Ofcourse,correctionsfo rcompressibility,wakeshadow,displacementblocking,ands oforth,mustbemadeasf o rtheforcetests,butjet-boundaryandallnement-anglecorrectionstothedragareunnecessary.Jet-boundaryandalinement-anglecorrectionsareappliedt otheangleo fattack.


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NACAARRNo.L4E31 5correctionsappliedareaccurate,thisprofiledragshouldcheckthatdeterminedfrom wakesurveysacrosstheentirewing. Thisprocedurewouldalsobeexpectedt obemostreliableatlo wliftcoefficientsbecausei tdependsupontheaccuratecalculationoftheInduceddrag. Athighliftcoefficients,anadditionalsourceofinaccuracyIsthedifficultyo fmakingprofile-dragmeasurementsIntheregiono ftheairfoiltip.

EXAMPLESOPCURRENTPRACTICELangley19-foo tpressuretunnel. -ThecalibrationandcorrectionprocedureusedintheLangley19-footpressuretunnelfollowscloselytheprocedureoutlineda scorrectionmethodA . TaretestsaremadewiththemodelmountedInverted,thenormalsupportsusedastaresupports,andaseto fexact-Imagedummysupports

mountedo ntheoppositesideo fthemodel.Inasmuchasthestatic-pressuregradientatthepositionofthemodeli sessentiallyzero,nobuoyancycorrectionsarenecessary. Total-pressuresurveys


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36 ACAARRNo .L4E31themodelInvertedo nthisnormalsupportstrutandusingadummystrutthatisanimageo fthelowerstrut. ItI sunnecessarytoconvertthetarestocoefficientf ormbeforetheirapplicationtothemodeldatabecauseaconstantpredetermineddynamicpressurecanbemaintained. Taremomentsmust,however,betransferredhroughthemodelbeforetheyareapplied.

Allnement-angletestsareno trunforeachmodelbutarerunwithtw ostandardwingsofdifferentspansandcheckedoccasionally. Becausethevariationin eacrossthetunnelisnotenoughtoshowanydifferenceforthetwostandardwings,theweightingprocedurefordifferentwingplanformsI snotnecessary. Changesoftheorderof0,2intheallnementanglehavebeennotedoveraperiodofseveralyears. Thenecessityo fperiodicchecktestsi sthusindicated. Theaccuracyofthedragbalancemakespossiblethedeterminationo ftheallnementangletowithinabout0.05. Theimpor-tanceofexactlyreproducingthetunnelleakagecondi-tionsfo ralinement-angleandtaretestswasdemonstratedintheLangley7-by10-foottunnelwhenalinement-angletestswererunafteranewstreamlinefairinghadbeenaddedtothesupportstrut. Testsmadewiththelower


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NACAARRNo .L4E31 7incorrectingthedataisthatobtainedfromtheyaw-headsurveyswithsupportsinplace.

Severalmethodsareusedfordeterminingtares.Onemethodusedi sthatdescribedpreviouslyforcorrectionmethod B ,inwhichthetaresaredeterminedintwoparts(reference19). Anothermethodusedfre-quentlyatpresentformeasuringdragtaresisthewake-curvey method. ThenormalsupportstrutsInthistunnelareusuallyattachedtotheundersurfaceo fthewing. V I alee-surveymeasurementsoftheprofiledragaremadeatanumbero fspanwisestationsandverysmallIntervalsareused n e - c i rthesupport-strutlocation. Asmoothcurvei sobtainedforthevariationofprofiledragalongthewingatsomedistancefromthesupport.Asthesupporti sapproached,thedragrisesconsiderably.Itisassumedthatthewingprofiledragwillshowauniform variation;therefore,acurveisarbitrarilyfaired,andthosepointsnearthesupportareneglected.Theintegrateddifferencebetweenthiscurveandthatdrawnthroughthemeasuredvaluesofprofiledraggivesthetare.


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38 ACAARRNo .L4E31

Thecorrectionforwakeblockingi sno wobtained bymeasuringthetotalpressureaheado fa modelandthestaticpressure5nthetestchamber,whichi sequalt ot h estaticpressurea tthemodelposition,andapplyingBernoulli'stheoremt oobtainthefree-streamdynamicpressure.Buoyancycorrectionsarenotnecessaryforplain-wingmodelsmountedintheusualposition. Ifthe

modeltobetestedhasafuselage,however,buoyancycorrectionsarerequired.Measurementshaveshownthattheeffectoftheexitconeo fthistunnelontheairflowbehinda modeli so fapproximatelythesamemagnitudeasandofoppositesignfromthatduetojet-boundaryinterference.Thepitching-momentcorrectionsthatarerequiredtoaccountfo rthejet-boundaryinterferencearethus

usually negligible.CONCLUDINGR E ' / ; A R K C


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NACAARRNo .L4E31 9Theaccuracytowhichthecorrectionsmustbedeter-minedandthetimeto hespentincalibratingthetunnelmustultimately hedecided bythetunneloperatorfromconsiderationsofthepurposeforwhichthetestsarebeingconducted,theprecisionrequiredinthefinalresults,andthetimeavailablefordeterminingandapplyingthecorrections.

LangleyMemorialAeronauticalLaboratoryNationalAdvisoryCommitteef o rAeronauticsLangleyField,Va.


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40 ACAARRNo .L4E31

REFERENCES1 .lein,ArthurL. ,Serrell,PeterV .H. ,andMillikan,ClarkP.: ANewTwo-ParameterModelSuspensionSystemfo rtheGalcit10-Pt.WindTunnel. Jour.Aero.Sei.,vol.9 ,no.8 ,June1942,pp.302-308.2 .auert,H. :indTunnelInterferenceo n Wings,

Bodies,and Airscrews. R .& M .No .1566,A.R.G.(British),1933.3 .auert,H. : TheEffecto ftheStaticPressureGradientontheDragofa Body TestedinaWindTunnel. R .&M .No .1158,JUR.C-(British),1928.4 .heodorsen,Theodore,andSilverstein,Abe: Experi-mentalVerificationo ftheTheoryof Wind-Tunnel

BoundaryInterference. NACARep.No .478,1934.5 .night,Montgomery,andHarris,ThomasA. : Experi-mentalDeterminationo fJetBoundaryCorrectionsforAirfoilTestsinPourOpen WindTunnelJets


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NACAARRNo .L4E31 1

11.otz,Irmgard: CorrectionofDownwashinWindTunnelso fCircularandEllipticSections.MACATMNo .801,1936.12 .avin,J .G. ,Jr.,andHensel,R .W. : EllipticTunnel-WallCorrectionso nDragandStall.Jour.Aero.Sei.,vol.9 ,no .14,Dec.1942,pp.533-537.13.tewart,H .J . : ACorrectiontotheYawingMomentDuet oAileronsfo rCircularWindTunnels. Jour.Aero.Sei.,vol.6 ,no.8 ,June1939,pp.329-331.14.atzoff,S . ,andFinn,RobertS . : DeterminationofJet-BoundaryCorrectionstoCowling-Flap-OutletPressuresby an ElectricalAnalogyMethod. NACAARRNo.4B23,1944.15.ilverstein,Abe,Katzoff,S. ,andBullivant,W.Kenneth: Downwashand- f a k ebehindPlainandFlappedAirfoils. NACARep.No .651,1939.16 .ckert,3.:xperienceswithFlow-Direction


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42 ACAARRNo .L4E31BIBLIOGRAPHY

Bradfield,P .B. : The5-Pt.OpenJetWindTunnel,R.A.E.R ,& M .No .1364,A.R.C(British),1931.Cowley,W.L. ,andMcMillan,G .A. : Effecto fV / i n dTunnelWallInterferenceo nthePitchingMomentsofLargeModelsintheDuplexTunnel. R .&M .No.1639,A.R.C.(British),1935.Cowley,W.L. ,andJones,L .J . :nExperimentalTestofthePrandtlCorrectionforTunnelWallInterfer-ence, R . S r M ,No.898,A.R.C.i.(British),1924.Davison,B. ,andRosenhead,L. ; WindTunnelCorrectionfo raCii'cularOpenJetTunnelwithaReflexionPlate. Proc.Roy.Soc.(London),ser.A ,vol.177,no .970,Feb.24,1941,pp.366-382.Dryden,H .L. ,andReald,R .H. ; InvestigationofTurbu-lenceinWindTunnelsbyaStudyofthePlowaboutCylinders. NACARep.No.231,1926.


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NACAARRNo .L4E31 3Glauert,I T . : SomeGeneralTheoremsConcerningWind

TunnelInterferenceo nAerofoils. R .&M .No .1470,A.R.C.(British),1932.Glauert,I T . : -TheInterferenceo ntheCharacteristicsofanAerofoilInaWindTunnelo fRectangularSection. R .&M .N o .1459,A.R.C.(British),1932,Glauert,H. ,andHartshorn,A .S . : TheInterferenceo fWindChannelWallsontheDownwashAngleandtheTail-

settingt oTrim. R ,&M .No .947,A.R.C.(British),Harris,ThomasA . : The7by10Fo otWindTunnelo ftheNationalAdvisoryCommitteefo rAeronautics. NACARep.No .412,1931.Higgins,GeorgeJ . : WallInterferenceinClosedTypeWindTunnels. NACATNNo .256,1927.Jacobs,EastmanN. : SphereDragTestsIntheVariableDensityWindTunnel. NACATNNo .312,1929.Jacobs,EastmanN. ,andAbbott,IraF. : AirfoilSection


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44 ACAAHRNo .L4E31Stewart,H .J . : TheEffecto f Wind TunnelWallInter-

ferenceontheStallingCharacteristicsofWings.Jour.Aero.Sei.,vol.8 ,no.11,Sept.1941,pp.426-428.Terazawa,Kwan-ichi: OntheInterferenceo fWindTunnelWallso fRectangularCross-SectionontheAerodynamicalCharacteristics " o fa Wing. Rep.No .44(vol.IV),Aero.Res.Inst.,TokyoImperialUniv., Oct.1928,pp.69-81.Theodorsen,Theodore; TheTheoryo fWind-TunnelWallInterference. NACARep.No.410,1931.Theodorsen,Theodore: Interferenceo nanAirfoilofFiniteSpanInanOpenRectangularWindTunnel.NACARep.No.461,1933.


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NACAARRNo.L4E31 45

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T1TU Wind-TunnelCalibrationan dCorrectionProceduresforTfcree-DimenslonaiModelsAUTHOR(S]OR1S.GENCY PU8USHWBY

Swanson,R.S.;CUlls.C.L.LangleyMemorialAeronauticalLab.,Lt&gleyAirForceBase,V a. NationalAdvisoryCommitteeforAeronautics,Washington,D.C .(No

VST-fiEff.M8KIM ONn

U.S. English lUimunotGphotos,table,diiRr,drwgsDetailedmethodsarepresentedordeterminingwind-tunnelcorrectionsforeffectsofmodel-supportsystem,nonunilormairflownunnel,ndtunnelwalloretboundaries.Proceduresarellustratedby equations. Requiredestsarediscussed. Specialatten-tionIsgiventodragmeasurements.wogeneralmethodsusedfordeterminingand applyingcorrectionstoforcetests,andcorrectionproceduresforwalcesurveyestsarediscussed.Methodsapplyonlytotestsatsubcrltlcalspeeds.

DISTRIBUTION: SPECIAL. AllrequestsforcopiesmustbeaddressedoPuhlishlngAgencyDIVISION:SECTION: CaWOTanotr (2)0AT IHEETNO.:

SUBJECTHEADINGS:Windtunnels Boundaryeffect(99110.3)Windtunnelmounts Effecton tests(99070)CentralAi rDtfmHiOfflcQ Wrip S MuniAirNrcaOo*o,Ovjrron.Ohio % \INDEX

wind tunnel calibration

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